Burking was a very specific form of murder for money- the killing of suitable specimens for medical research. No doubt it comes from one of its most famous practitioners, William Burke of Burke and Hare fame.
I found out about the name because of a historian’s claim that two of the most highly regarded pioneers of obstetrics, William Hunter and William Smellie (what is it with the Williams, Hare was one as well), may have ordered freshly murdered pregnant women to help their research and run up a body count greater than Burke and Hare and Jack the Ripper combined.
On the subject of Burke and Hare, there’s a graphic novel about them which has been getting some good reviews. I haven’t read it yet, but it’s going on to my (admittedly long) list of books I should get. Buy Burke and Hare from Amazon.